Stochastic Sensitivity Analysis Research Articles

Analysis of noise effects in a map-based neuron model with Canard-type quasiperiodic oscillations

A problem of the mathematical modeling and analysis of the complex mixed-mode stochastic oscillations in neural activity is studied. For the description of noise-induced transitions between regimes of neuron dynamics, 2D map-based system near Neimark–Sacker bifurcation is used as a conceptual model. We focus on the parametric zone of Canard explosion where the attractors (closed invariant curves) are extremely sensitive to noise. Using direct numerical simulation and semi-analytical approach based on the stochastic sensitivity analysis, we study the noise-induced transformations from unimodal oscillations to bimodal spiking oscillations. The supersensitive invariant curve which marks the epicenter of the Canard explosion is found. It is shown that for this curve, the noise-induced splitting occurs for extremely small random forcing. Changes of the amplitude and frequency properties of the stochastic mixed-mode oscillations are studied. The phenomenon of noise-induced transitions from order to chaos is discussed.

Stochastic Sensitivity Synthesis in Discrete-Time Systems with Parametric Noise

Abstract Discrete nonlinear stochastic systems with general parametric noises are considered. To approximate the dispersion of random states, we propose an asymptotic approach based on the stochastic sensitivity analysis. This approach is used for the solution of the stabilization problem for the discrete controlled systems forced by parametric noise. A theory of the synthesis of the stochastic sensitivity by the feedback regulators is elaborated. Regulators minimizing the stochastic sensitivity are used in the problem of the structural stabilization of equilibrium regimes in population dynamics. The efficiency of this technique is demonstrated on the example of the suppression of undesired noisy large-amplitude regular and chaotic oscillations in the Hassell population model.

Stochastic uncertainty quantification for safety verification applications in nuclear power plants

There is an increasing interest in computational reactor safety analysis to systematically replace the conservative calculations by best estimate calculations augmented by quantitative uncertainty analysis methods. This has been necessitated by recent regulatory requirements that have permitted the use of such methods in reactor safety analysis. Stochastic uncertainty quantification methods have shown great promise as they are better suited to capture the complexities in real engineering problems. With advances in computational capabilities in recent times, these methods when utilized would provide distributions of safety important parameters computed by thermal hydraulic codes. In this study, a transient is simulated with a best estimate thermal hydraulic code, CATHENA. Stochastic uncertainty quantification and sensitivity analysis were performed using the OPENCOSSAN software which is based on the Monte Carlo method. The uncertainty and sensitivity analyses results were then utilized to update the dynamic Fault Semantic Network for safety verification. The effect of uncertainty in two input parameters (initial temperature and pressure) was investigated by analyzing the probability distribution of two output parameters. The first four moments of the output pressure and fuel pin temperature were computed and analyzed. The uncertainty in output pressure was 0.087% and 0.048% was found for the fuel pin temperature. These results are expected to provide insight for safety analyses by their utilization in updating the dynamic FSN.

Polymorphic uncertainty quantification for stability analysis of fluid saturated soil and earth structures

AbstractNowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors. These can be distinguished into aleatoric (e.g. model parameters) and epistemic (e.g. numerical approximation) uncertainties. In order to get access to a risk assessment, these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In our subproject, which is part of the SPP 1886 (sp12), the focus is driven on quantification and assessment of polymorphic uncertainties in computational simulations of earth structures, especially for fluid‐saturated soils. To describe the strongly coupled solid‐fluid response behavior, the theory of porous media (TPM) will be used and prepared within the framework of the finite element method (FEM) for the numerical solution of initial and boundary value problems [2, 3]. To capture the impacts of different uncertainties on computational results, two promising approaches of analytical and stochastic sensitivity analysis will enhance the deterministic structural analysis [6–8]. A simple consolidation problem already provided a high sensitivity in the computational results towards variation of material parameters and initial values. The variational and probabilistic sensitivity analyses enable to quantify these sensitivities. The variational sensitivities are used as a tool for optimization procedures and capture the impact of different parameters as continuous functions. An advantage is the accurate approximation of the solution space and the efficient computation time, a disadvantage lies in the analytical derivation and algorithmic implementation. In the probabilistic sensitivity analysis from the field of statistics, the expense only increases proportionally to the problems dimension. Instead of a constant value, the model parameters are defined as probability distribution, which provides random values. Thus, a set of solution data is built up by several cycles of the simulation. Different approaches of the Bayes statistics will enable to receive accurate information with just a few simulations. The overall objective is the development of more efficient methods and tools for the sizing of earth structures in the long‐run. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Uncertainty‐conscious methodology for process performance assessment in biopharmaceutical drug product manufacturing

This work presents an uncertainty‐conscious methodology for the assessment of process performance—for example, run time—in the manufacturing of biopharmaceutical drug products. The methodology is presented as an activity model using the type 0 integrated definition (IDEF0) functional modeling method, which systematically interconnects information, tools, and activities. In executing the methodology, a hybrid stochastic–deterministic model that can reflect operational uncertainty in the assessment result is developed using Monte Carlo simulation. This model is used in a stochastic global sensitivity analysis to identify tasks that had large impacts on process performance under the existing operational uncertainty. Other factors are considered, such as the feasibility of process modification based on Good Manufacturing Practice, and tasks to be improved is identified as the overall output. In a case study on cleaning and sterilization processes, suggestions were produced that could reduce the mean total run time of the processes by up to 40%. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1272–1284, 2018

A health economic evaluation of needle-based confocal laser endomicroscopy for the diagnosis of pancreatic cysts.

Background and study aims The low sensitivity of endoscopic ultrasound-guided fine-needle aspiration (EUS-FNA), especially for the diagnosis of serous cystadenomas (SCAs), can be associated with diagnostic uncertainty that can regularly lead to unnecessary surgical procedures. Needle-based confocal laser endomicroscopy (nCLE) used with EUS-FNA improves diagnostic accuracy, helping to reduce unnecessary surgery and patient follow-up. This study was conducted to evaluate the economic benefit of EUS-FNA + nCLE. Patients and methods Probabilities used were derived from two studies representative of the two diagnostic strategies: a retrospective analysis of patients diagnosed by EUS-FNA alone and a prospective study of patients diagnosed by EUS-FNA + nCLE. Costs were based on French healthcare system rates; both private and public sector rates were included. A decision tree structure model used these probabilities and costs for two hypothetical cohorts of 1000 patients. Results EUS-FNA + nCLE resulted in a reduction of 23 % in the total rate of surgical intervention, which translated to a reduction in clinical costs of 13 % (public sector) and 14 % (private sector). Additionally, the reduced rate of surgery would save the lives of 4 in 1000 patients. A stochastic sensitivity analysis using 100 simulations showed that in all cases the number of interventions was less for EUS-FNA + nCLE than for EUS-FNA. There was also a reduction in the incidence of false negatives using EUS-FNA + nCLE. Conclusions EUS-FNA + nCLE results in significant economic benefits by reducing the incidence of misdiagnosis through improved diagnostic accuracy.

Stochastic sensitivity analysis of nitrogen pollution to climate change in a river basin with complex pollution sources.

It is increasingly recognized that climate change could impose both direct and indirect impacts on the quality of the water environment. Previous studies have mostly concentrated on evaluating the impacts of climate change on non-point source pollution in agricultural watersheds. Few studies have assessed the impacts of climate change on the water quality of river basins with complex point and non-point pollution sources. In view of the gap, this paper aims to establish a framework for stochastic assessment of the sensitivity of water quality to future climate change in a river basin with complex pollution sources. A sub-daily soil and water assessment tool (SWAT) model was developed to simulate the discharge, transport, and transformation of nitrogen from multiple point and non-point pollution sources in the upper Huai River basin of China. A weather generator was used to produce 50years of synthetic daily weather data series for all 25 combinations of precipitation (changes by -10, 0, 10, 20, and 30%) and temperature change (increases by 0, 1, 2, 3, and 4°C) scenarios. The generated daily rainfall series was disaggregated into the hourly scale and then used to drive the sub-daily SWAT model to simulate the nitrogen cycle under different climate change scenarios. Our results in the study region have indicated that (1) both total nitrogen (TN) loads and concentrations are insensitive to temperature change; (2) TN loads are highly sensitive to precipitation change, while TN concentrations are moderately sensitive; (3) the impacts of climate change on TN concentrations are more spatiotemporally variable than its impacts on TN loads; and (4) wide distributions of TN loads and TN concentrations under individual climate change scenario illustrate the important role of climatic variability in affecting water quality conditions. In summary, the large variability in SWAT simulation results within and between each climate change scenario highlights the uncertainty of the impacts of climate change and the need to incorporate extreme conditions in managing water environment and developing climate change adaptation and mitigation strategies.

Stochastic sensitivity analysis of nonautonomous nonlinear systems subjected to Poisson white noise

The stochastic sensitivity function (SSF) method is extended to estimate the stationary probability distribution around periodic attractors of nonautonomous nonlinear dynamical systems subjected to Poisson white noise in this paper. After deriving the stochastic sensitivity functions of period-N cycle of mapping systems based on the characteristic of Poisson process, non-autonomous dynamical systems around periodic attractors are converted to mapping systems by constructing a stroboscopic map, and then the stochastic sensitivity functions of periodic attractors of nonautonomous nonlinear systems can be obtained by adopting the results of mapping systems. It is found that the stochastic sensitivity functions depend on the product of noise intensity and the arrival rate of Poisson processes. To illustrate the validity of the proposed method, a Henon map driven by Poisson processes and a Mathieu–Duffing oscillator under Poisson white noise are studied.

Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach

Engineering analyses of structures may be confronted with many sources of uncertainty, which may be of different types, such as parametric uncertainties versus modeling errors, and which may pertain to different structural components when complex structures are analyzed. Soize, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, Int. J. Numer. Meth. Eng., 81:939–970, 2010 has recently introduced a generalized probabilistic modeling approach, which can individually represent parametric uncertainties and modeling errors and which can individually represent sources of uncertainty pertaining to different structural components of complex structures. In this paper, we propose to augment this generalized probabilistic modeling approach with a stochastic sensitivity analysis in order to quantify and gain insight into separate impacts of distinct sources of uncertainty on quantities of interest. We demonstrate the proposed methodology by applying it to two computational-mechanics models involving uncertainty.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Global sensitivity analysis as a support for the generation of simplified building stock energy models

Buildings are responsible for 40% of total final energy consumptions in Europe. Numerous bottom-up models were recently developed to support local authorities in assessing the energy consumption of large building stocks and reduction potentials. However, current models rarely consider uncertainty associated to building usage and characteristics within the stock, resulting in potentially biased results.This study presents a generic model simplification approach using uncertainty propagation and stochastic sensitivity analysis to derive fast simplified (surrogate) models to estimate the current building stock energy use for improved urban planning. The methodology includes an engineering-based energy model as input to global sensitivity analysis (GSA) using the elementary effects (EE) screening and Sobol’ method for key parameters identification and regression analysis to derive simplified models for entire building stocks.The application to the housing stock of Esch-sur-Alzette (Luxembourg) showed that the parameters explaining most of the variability in final energy use for heating and domestic hot water are floor area, set-point temperature, external walls U-values, windows and heating system type. Results of the simplified models were validated against measured data and confirmed the validity of the approach for a simple yet robust assessment of the building stock energy use considering uncertainty and variability.

Effects of environmental factors on electric vehicle energy consumption: a sensitivity analysis

This study provides a detailed deterministic and stochastic sensitivity analysis of the propulsion energy cost of electric vehicles (EVs) with respect to environmental variables. In particular, the effects of wind speed, rolling resistance, parasitic power and temperature are highlighted. The study provides exact analytical expressions as well as simulations to illustrate the key results. It is shown that the sensitivity of energy consumption with respect to the four environmental variables greatly vary with operating conditions of the vehicle. These environmental effects can have a profound effect on the overall energy consumption of EVs and drastically affect range. The significance of the authors' findings for vehicle range estimation is discussed and potential avenues to exploit the strong dependency between propulsion energy and environmental factors are proposed.

Stochastic sensitivity analysis of concentration measures

The paper extends the traditional approach to measuring market concentration by embracing an element of stochasticity that should reflect the analyst’s uncertainty associated with the future development regarding concentration on the market. Whereas conventional practice relies on deterministic assessments of a market concentration measure with the use of current market shares, this says nothing about possible changes that may happen even in a near future. The paper proposes to model the analyst’s beliefs by dint of a suitable joint probability distribution for future market shares and demonstrates how this analytic framework may be employed for regulatory purposes. A total of four candidates for the joint probability distribution of market shares are considered—the Dirichlet distribution, the conditional normal distribution, the Gaussian copula with conditional beta marginals and the predictive distribution arising from the market share attraction model—and it is shown how their hyperparameters can be elicited so that a minimum burden is placed on the analyst. The proposed procedure for stochastic sensitivity analysis of concentration measures is demonstrated in a case study oriented on the Slovak banking sector.

Preventing Noise-Induced Extinction in Discrete Population Models

A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.

Stochastic sensitivity analysis of large-eddy simulation predictions of the flow around a 5:1 rectangular cylinder

A stochastic analysis of the sensitivity to grid resolution and modeling of large-eddy simulations (LES) results is carried out for the flow around a 5:1 rectangular cylinder, which is the object of an international benchmark (BARC) collecting experimental and numerical flow realizations. Significant dispersion of the BARC predictions was observed for some quantities, also in LES, and deterministic sensitivity analyses were not conclusive. LES are carried out here by using a spectral-element numerical method. An explicit quadratic low-pass filter in the modal space is used, characterized by a cut-off value and by a weight function, which provides dissipation of the modes higher than the cut off and acts as a SGS dissipation. The uncertain parameters are the size of the spectral elements in the spanwise direction and the weight of the explicit filter. The impact of the uncertainty in these parameters is evaluated through generalized polynomial chaos. The analysis is repeated for two different grid resolutions in the streamwise and lateral directions. The most-probable values and the stochastic variance of the results are compared with the ensemble average and with the overall dispersion of the BARC predictions respectively.

Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations

Abstract We study noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations. To study these transitions parametrically, we suggest a generalized mathematical technique using stochastic sensitivity functions and confidence domains for randomly forced equilibria, cycles, and chaotic attractors. This technique is demonstrated in detail for the simple one-dimensional stochastic system, in which points of crisis and tangent bifurcations are borders of the order window lying between two chaotic parametric zones. A stochastic phenomenon of the extension and shift of this window towards crisis bifurcation point, under increasing noise, is presented and analyzed. Shifts of borders of this order window are found as functions of the noise intensity. By our analytical approach based on stochastic sensitivity functions, we construct a parametric diagram of chaotic and regular regimes for the stochastically forced system.

Stochastic Sensitivity Analysis for a Competitive Turbidostat Model with Inhibitory Nutrients

A stochastic model of turbidostat in which two microorganism species compete for an inhibitory growth-limiting nutrient is considered. In the deterministic case, the model has rich dynamics: a coexistence equilibrium and the washout equilibrium can be simultaneously stable, and a stable limit cycle may exist. In the stochastic case, a phenomenon of noise-induced extinction occurs. Namely, the stochastic trajectory near the deterministic coexistence equilibrium will tend to the washout equilibrium. Based on the stochastic sensitivity function technique, in this paper, we construct the confidence ellipse and then estimate the critical value of the intensity for noise generating a transition from coexistence to extinction. We also construct the confidence band to find the configurational arrangement of the stochastic cycle.

Time-independent stochastic design sensitivity analysis of structural systems with second-order accuracy

In the paper, the static sensitivity of complex structures with respect to random design parameters is presented. Using the adjoint system method, based on the mean-point second-order perturbation method, the first two probabilistic moments of time-independent sensitivity are formulated with means and cross-covariances of random design parameters as the input data. It enables one to obtain the second-order accuracy of the solution. The presented formulations are illustrated by a number of numerical examples. The influence of finite element mesh density for the obtained results is discussed using the analysis of the spatial bar dome.

Stochastic sensitivity analysis for structural dynamics systems via the second-order perturbation

The problem of dynamic structural response dependent on random variations of design parameters is presented in the paper. A variational formulation of the FEM equations of motion and the probability distribution of time instant stochastic sensitivity are described. The suggested perturbation technique is completely second-order accurate, unlike in conventional approach. For instance, three different structural systems, excited by a Heaviside impact, are implemented and discussed. Numerical results for the first two probabilistic moments of displacement sensitivity gradients are obtained by the mode superposition method. Concluding remarks show that dynamic sensitivity analysis in the stochastic context better describes the real structural response and allows us to find the appropriate design point.

Stochastic Sensitivity Analysis and Noise-Induced Chaos in 2D Logistic-Type Model

We study the dynamics of stochastically forced 2D logistic-type discrete model. Under random disturbances, stochastic trajectories leaving deterministic attractors can form complex dynamic regimes that have no analogue in the deterministic case. In this paper, we analyze an impact of the random noise on 2D logistic-type model in the bistability zones with coexisting attractors (equilibria, closed invariant curves, discrete cycles). For the constructive probabilistic analysis of the random states distribution around such attractors, a stochastic sensitivity functions technique and method of confidence domains are used. For the considered model, on the base of the suggested approach, a phenomenon of noise-induced transitions between attractors and the generation of chaos are analyzed.